Precis of my book by this title, for a symposium.

‘‘Thus I believe that there is no part of matter which is not—I do not say divisible—but actually divided; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.’’ (Leibniz, letter to Foucher).

Hud Hudson presents an innovative view of the metaphysics of human persons according to which human persons are material objects but not human organisms. In developing his account, he formulates and defends a unique collection of positions on parthood, persistence, vagueness, composition, identity, and various puzzles of material constitution. The author also applies his materialist metaphysics to issues in ethics and in the philosophy of religion. He examines the implications for ethics of his metaphysical views for standard arguments addressing the (...) moral permissibility of our treatment of human persons and their parts, fetuses and infants, the irreversibly comatose, and corpses. He argues that his metaphysics provides the best foundation in the philosophy of religion for the Christian doctrine of the resurrection of the body. Hudson addresses a broad range of metaphysical issues, but among his most strikingly original contributions are his defense of the "Partist" view and his argument for the compatibility of Christianity with a materialistic theory of human persons. (shrink)

John Hawthorne is widely regarded as one of the finest philosophers working today. He is perhaps best known for his contributions to metaphysics, and this volume collects his most notable papers in this field. Hawthorne offers original treatments of fundamental topics in philosophy, including identity, ontology, vagueness, and causation. Six of the essays appear here for the first time, and there is a valuable introduction to guide the reader through the selection.

I argue that extended simples are possible. The argument given here parallels an argument given elsewhere for the claim that the shape properties of material objects are extrinsic, not intrinsic as is commonly supposed. In the final section of the paper, I show that if the shape properties of material objects are extrinsic, the most popular argument against extended simples fails.

Background and assumptions. Persistence and philosophy of time ; Atomism and composition ; Scope ; Some matters of methodology -- Persistence, location, and multilocation in spacetime. Endurance, perdurance, exdurance : some pictures ; More pictures ; Temporal modification and the "problem of temporary intrinsics" ; Persistence, location and multilocation in generic spacetime ; An alternative classification -- Classical and relativistic spacetime. Newtonian spacetime ; Neo-Newtonian (Galilean) spacetime ; Reference frames and coordinate systems ; Galilean transformations in spacetime ; Special relativistic (...) spacetime ; Length contraction and time dilation ; Invariant properties of special relativistic spacetime -- Persisting objects in classical spacetime. Enduring, perduring, and exduring objects in Galilean spacetime ; The argument from vagueness ; From minimal D-fusions to temporal parts ; Motivating a sharp cutoff ; Some objections and replies ; Implications -- Persisting objects in Minkowski spacetime. Enduring, perduring, and exduring objects in Minkowski spacetime ; Flat and curved achronal regions in Minkowski spacetime ; Early reflections on persisting objects in Minkowski spacetime : Quine and Smart ; "Profligate ontology"? ; Is achronal universalism tenable in Minkowski spacetime? ; "Crisscrossing" and immanent causation -- Coexistence in spacetime. The notion of coexistence ; Desiderata ; Coexistence in Galilean spacetime ; Coexistence in Minkowski spacetime : CASH ; Alexandrov-Stein present and Alexandrov-Stein coexistence ; AS-Coexistence v. CASH : symmetry, multigrade, and objectivity ; As-coexistence v. CASH : relevance ; The mixed past of coexistence ; No need in the extended now -- Strange coexistence? Coexistence and existence@ ; The asymmetry thesis ; The absurdity thesis ; Collective CASH value of coexistence ; Collective existence@ and coexistence in classical spacetime ; Collective existence@ and coexistence in Minkowski spacetime ; Contextuality ; Chronological incoherence ; Some objections -- Shapes and other arrangements in Minkowski spacetime. How rigid is a granite block? ; Perspectives in space ; Perspectives in spacetime ; Are shapes intrinsic to objects? ; The causal objection ; The micro-reductive objection ; Pegs, boards, and shapes ; Perduring objects exist. (shrink)

This chapter argues that from a particularly weak recombination principle and plausible assumptions about the nature of parthood and location, it follows that it is possible that the mereological structure of the material world and that of space-time fail to correspond to one another in very radical ways. The chapter suggests, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of no less unappealing alternatives. It also discusses a few ways in which their possibility (...) is relevant to various important debates in metaphysics. (shrink)

This paper develops an endurantist theory of persistence. The theory is built around one basic tenet, which concerns existence at a time – the relation between an object and the times at which that object is present. According to this tenet, which I call transcendentism, for an object to exist at a time is for it to participate in events that are located at that time. I argue that transcendentism is a semantically grounded and metaphysically fruitful. It is semantically grounded, (...) insofar as a semantic analysis of our temporal talk favors it over rivals. It is metaphysically fruitful, insofar as the theory of persistence that can be built around it – the transcendentist theory of persistence, to give it a name – requires neither temporal parts nor the problematic commitments to which all extant forms of endurantism are committed, such as the possibility of extended simples or multilocation. (shrink)

The following quotation, from Frank Jackson, is the beginning of a typical exposition of the debate between those metaphysicians who believe in temporal parts, and those who do not: The dispute between three-dimensionalism and four-dimensionalism, or more precisely, that part of the dispute we will be concerned with, concerns what persistence, and correllatively, what change, comes to. Three-dimensionalism holds that an object exists at a time by being wholly present at that time, and, accordingly, that it persists if it is (...) wholly present at more than one time. For short, it persists by enduring. Four-dimensionalism holds that an object exists at a time by having a temporal part at that time, and it persists if it has distinct temporal parts at more than one time. For short, it persists by perduring. In the light of these comments, some readers will perhaps find the question that forms the title of this paper a little puzzling. They may have learned to use the terms ‘fourdimensionalism’ ‘perdurantism’ and ‘belief in temporal parts’ interchangeably; or perhaps even to define one in terms of the other. Such a usage, however, is inapposite. We might imagine a Flatland-like world of two spatial dimensions and one temporal, whose philosophers are divided between a theory of persistence on which they persist by having temporal parts, and a theory on which they persist by being wholly located in each of several times. This is just the same issue we face, but at least the label ‘four-dimensionalism’ seems inapposite: the four-dimensionalist Flatlanders believe in only three dimensions! (shrink)

I formulate a theory of persistence in the endurantist family and pose a problem for the conjunction of this theory with orthodox versions of special or general relativity. The problem centers around the question: Where are things?

Thomas Sattig develops a comprehensive framework for doing philosophy of time, and offers an original three-dimensionalist picture of the material world. He brings together a variety of different perspectives, linking our ordinary conception of time with the physicist's conception, and linking metaphysical questions about time with questions in the philosophy of language.

We attempt to extend the nominalistic project initiated in Hartry Field's Science Without Numbers to modern physical theories based in differential geometry.

The notion of multiple location plays an important role in the characterization of endurantism. Several authors have recently offered cases intended to demonstrate the incoherence of multiple location. I argue that these cases do not succeed in making multiple location problematic. Along the way, several crucial issues about multiple location and its use by endurantists are clarified.

We have two aims in this paper. The first is to provide the reader with a critical guide to recent work on relativity and persistence by Balashov, Gilmore and others. Much of this work investigates whether endurantism can be sustained in the context of relativity. Several arguments have been advanced that aim to show that it cannot. We find these unpersuasive, and will add our own criticisms to those we review. Our second aim, which complements the first, is to demarcate (...) the most defensible form of relativistic endurantism. A recurring theme of this paper is that even those philosophers who do worry about relativity have not taken it seriously enough. (shrink)

The terms `endurance' and `perdurance' are commonly thought to denote distinct ways for an object to persist, but it is surprisingly hard to say what these are. The common approach, defining them in terms of temporal parts, is mistaken, because it does not lead to two coherent philosophical alternatives: endurance so understood becomes conceptually incoherent, while perdurance becomes not just true but a conceptual truth. Instead, we propose a different way to articulate the distinction, in terms of identity rather than (...) temporal parts: an object endures if its identity is determined at every moment at which it exists. We make precise what it means for the identity of an object to be determined at a moment. We also discuss what role the endurance / perdurance distinction, so understood, should play in the debates about time, material objects and personal identity. (shrink)

Yuri Balashov sets out major rival views of persistence--endurance, perdurance, and exdurance--in a spacetime framework and proceeds to investigate the implications of Einstein's theory of relativity for the debate about persistence. His overall conclusion--that relativistic considerations favour four-dimensionalism over three-dimensionalism--is hardly surprising. It is, however, anything but trivial. Contrary to a common misconception, there is no straightforward argument from relativity to four-dimensionalism. The issues involved are complex, and the debate is closely entangled with a number of other philosophical disputes, including (...) those about the nature and ontology of time, parts and wholes, material constitution, causation and properties, and vagueness. (shrink)

Multilocation and Minimal Mereology do not mix well. It has been pointed out that Three-Dimensionalism, which can be construed as multilocation-friendly, runs into trouble with Weak Supplementation. But in fact, regardless of one’s theory of persistence, if someone posits the possibility of any one of several kinds of multilocation, he or she will not be able to maintain the necessity of any of the three axioms of Minimal Mereology: the Transitivity of Proper Parthood, the Asymmetry of Proper Parthood, and Weak (...) Supplementation. In fact, positing even the mere conceivability of cases involving multilocation will require the denial of the analyticity of Minimal Mereology. In response to this, some have claimed that we ought to relativise parthood, either to one region or to two. Unfortunately, if we replace the axioms of Minimal Mereology with region-relativised counterparts, we will not be able to capture the intuitions that supported the original axioms. The only adequate solution, I maintain, is to restrict multilocation to a domain outside the scope of the rules we intuitively take to govern the parthood relation. For those who take Minimal Mereology to be necessary and universal, that will mean relinquishing the possibility of multilocation. (shrink)

I argue that from a very weak recombination principle and plausible assumptions about the nature of parthood and location it follows that it's possible that the mereological structure of the material world and that of spacetime fail to correspond to one another in very radical ways. I defend, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of equally radical alternatives. I also discuss a few ways in which their possibility is relevant to various (...) debates in metaphysics. (shrink)

This paper presents the strongest version of a non-perdurantist four-dimensionalism: a theory according to which persisting objects are four-dimensionally extended in space-time, but not in virtue of having maximal temporal parts. The aims of considering such a view are twofold. First, to evaluate whether such an account could provide a plausible middle ground between the two main competitor accounts of persistence: three-dimensionalism and perdurantist four-dimensionalism. Second, to see what light such a theory sheds on the debate between these two competitor (...) theories. I conclude that despite prima facie reasons to suppose that non-perdurantist four-dimensionalism might be a credible alternative to either other account of persistence, ultimately the view is unsuccessful. The reasons for its failure illuminate the sometimes stagnant debate between three-dimensionalists and perdurantists, providing new reasons to prefer a perdurantist metaphysics. (shrink)

Existing puzzles about coinciding objects can be divided into two types, corresponding to the manner in which they bear upon the endurantism v. perdurantism debate. Puzzles of the first type, which involve temporary spatial co-location, can be solved simply by abandoning endurantism in favor of perdurantism, whereas those of the second type, which involve career-long spatial co-location, remain equally puzzling on both views. I show that the possibility of backward time travel would give rise to a new type of puzzle. (...) The new puzzles confront perdurantists and can be solved just by shifting to endurantism. (shrink)

A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...) functions and those that do correspond to continuous functions. (shrink)

Recently, Cody Gilmore has deployed an ingenious case involving backwards time travel to highlight an apparent conflict between the theory that objects persist by perduring, and the thesis that wholly coincident objects are impossible. However, careful attention to the concepts of location and parthood that Gilmore’s cases involve shows that the perdurantist faces no genuine objection from these cases, and that the perdurantist has a number of plausible and dialectically appropriate ways to avoid the supposed conflict.

This article discusses two arguments in favor of perdurance. The first is Sider’s argument from vagueness, “one of the most powerful” in favor of perdurantism. I make the observation that endurantists have principled grounds to claim that the argument is unsound, at least if endurance is formulated in locative rather than mereological terms. Having made this observation, I use it to emphasize a somewhat neglected difference between endurantists and perdurantists with respect to their views on material objects. These views, in (...) the case of endurantists, lead to a further, less than conclusive but nevertheless interesting argument against endurantism—the anti-fundamentality argument—which I discuss and tentatively endorse. That argument posits that endurantists must take location to be a fundamental relation, and that this has as a consequence the metaphysical possibility of some rather unwelcome scenarios. Perdurantists may avoid this consequence by denying that location is fundamental, perhaps by embracing supersubstantivalism. (shrink)

I argue that it may well be the case that space and time do not consist of points, indeed that they have no smallest parts. I examine two different approaches to such pointless spaces : a topological approach and a measure theoretic approach. I argue in favor of the measure theoretic approach.

Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The (...) main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal."--P. [4] of cover. (shrink)

An introduction to the theories of endurantism and perdurantism, and persistence more broadly.

This paper takes a close look at the thought that mereological relations on material objects mirror, and are mirrored by, parallel mereological relations on their exact locations. This hypothesis is made more precise by means of a battery of principles from which more substantive consequences are derived. Mereological harmony turns out to entail, for example, that atomistic space is an inhospitable environment for material gunk or that Whiteheadian space is not a hospitable environment for unextended material atoms.

Endurantism, the view that material objects are wholly present at each moment of their careers, is under threat from supersubstantivalism, the view that material objects are identical to spacetime regions. I discuss three compromise positions. They are alike in that they all take material objects to be composed of spacetime points or regions without being identical to any such point or region. They differ in whether they permit multilocation and in whether they generate cases of mereologically coincident entities.

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.

The surviving sources on the Stoic theory of division reveal that the Stoics, particularly Chrysippus, believed that bodies, places and times were such that all of their parts themselves had proper parts. That is, bodies, places and times were composed of gunk. This realisation helps solve some long-standing puzzles about the Stoic theory of mixture and the Stoic attitude to the present.

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

Say that mereological harmony is the view that there is at least some mirroring between the mereological structure of material objects and the mereological structure of their locations: each, in some way, mirrors the other. As it turns out, there is a confusing array of systems of harmony available to the substantivalist. In this paper, I attempt to bring some order to these systems. I explore some systems found in the literature, as well as some natural systems which haven’t been (...) discussed. Along the way, I explore a number of metaphysical consequences of the different systems of harmony. The paper ends with a roadmap of possible views for the substantivalist. (shrink)

This chapter develops a three-dimensionalist account of temporal supervenience — the temporal-regions account — and argues that the latter shares the main virtues and avoids the main drawbacks of its four-dimensionalist rival. The three-dimensionalist account asserts and explains the theses that the facts of persistence logically supervene on facts about the spatiotemporal location of objects, and that the facts of temporal instantiation logically supervene on the atemporal instantiation of properties by temporally unextended spacetime regions occupied by objects. Structural similarities of (...) the temporal-regions account and the temporal-parts account are pointed out, and the temporal-regions account is shown to avoid the problems that threaten the temporal-parts account. The remainder of the chapter deals with various consequences and apparent difficulties of three-dimensionalist supervenience. (shrink)

Can material objects be weakly located at regions of spacetime and yet fail to be exactly located anywhere? In this paper, I discuss a case which, at least according to one interpretation, answers affirmatively: the case of blending gunky water and wine, in gunky space. Perhaps after such a blend, the water and wine aren't exactly located anywhere while being weakly located at the location of the blend and any region which overlaps it. I show that the case is interesting (...) and complicated, and has consequences for some ideas found in papers by Daniel Nolan and Josh Parsons. (shrink)

This chapter takes a close look at the thought that mereological relations on material objects mirror, and are mirrored by, parallel mereological relations on their exact locations. This hypothesis is made more precise by means of a battery of principles from which more substantive consequences are derived. Mereological harmony turns out to entail, for example, that atomistic space is an inhospitable environment for material gunk or that Whiteheadian space is not a hospitable environment for unextended material atoms.

Let us say that a thing is gunky just in case every part of that thing has proper parts. The idea that all physical objects are gunky seems sufficiently sweeping, interesting, and plausible that it is worth examining. However, there is a difficulty. The features of an extended object can surely vary continuously. If an object is gunky then it cannot have point-sized parts which have no further parts. But how can one conceive of a continuous variation in features other (...) than as the obtaining of different features at different point sized locations? (shrink)

This paper describes a plausible view of the nature of physical objects, their mereological connections to each other, and their relation to spacetime. As well as being parsimonious, the view provides a plausible context for denying all of the following: (1) A theory that objects endure through time (and do not have temporal parts, as normally conceived) cannot claim that material objects are identical to space-time regions they occupy. (2) At least one of the family of mereological connections (part-whole, overlap (...) etc.) is to be taken as primitive. (3) Claims entirely in the language of quantifiers and identity and mereology are not semantically vague. It is thus an example showing that the there are more options for the metaphysics of objects, spacetime and mereology than many metaphysicians ordinarily assume. (shrink)

There exist well‐known conundrums, such as measure‐theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space‐time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space‐time.